Limit Theorems for Deviation Means of Independent and Identically Distributed Random Variables

We derive a strong law of large numbers, central limit theorem, the iterated logarithm and deviation theorem for so-called means independent identically distributed random variables. (For we suppose only pairwise independence instead (total) independence.) The class is special M-estimators or more generally extremum estimators, which are well studied in statistics. assumptions our theorems seem to be new weaker than known ones literature. In particular, results on numbers generalize corresponding quasi-arithmetic due de Carvalho (Am Stat 70(3):270–274, 2016) Bajraktarević Barczy Burai (Aequ Math 96(2):279–305, 2022).